分数微积分在系统建模中的应用

Application of Fractional Calculus in System Modeling

介绍了分数微积分定义,并运用拉普拉斯变换法证明了分数阶线性常微分方程解的存在性和唯一性,并给出了其传递函数描述和状态方程描述.提出了分数阶线性常微分方程的两种求解方法:直接拉普拉斯变换法和状态空间法,并利用一个粘弹性系统的仿真实例证明了其有效性.

An introduction of the definitions of fractional calculus was given. Laplace transform method was used to verify the existence and uniqueness of the solutions of fractional-order linear differential equations with constant coefficients. And their transfer function representation and state-space representation were also given. The solutions of fractional-order linear differential equations with constant coefficients were given in two ways: the direct Laplace transform method and the state-space method. Finally, an example of a viscoelasticity system was given to show the effectiveness of the methods aforementioned.